We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and prove that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in three different examples.
翻译:我们研究了巴伊西亚最佳实验设计中预期公用事业功能的稳定性特性,在非参数环境下为这一问题提供了一个框架,并证明预期效用在可能扰动方面的趋同率,这一比率在设计空间上是统一的,在一般情况下的锐度表现为在特殊情况下证明约束较低。为了使问题更加具体,我们考虑非线性巴伊西亚人对高斯可能性的反向问题,并证明为一般案例提出的假设已经得到满足,并恢复了观察地图扰动方面的预期效用的稳定性。三个不同的例子从数字上显示了理论趋同率。